Finite element modeling of a laminar flexure bending mechanism for elliptically bent hard x-ray mirror

Using a compact laminar overconstrained flexure bending mechanism and a capacitive sensor array, a precision compact mirror bending mechanism for 300-mm long hard x-ray mirror has been designed and constructed to perform initial test for x-ray zoom optics as a part of an Argonne Laboratory-Directed Research and Development project at the Advanced Photon Source. A Finite Element Model (FEM) of the mirror bender was created with commercial simulation software. An iterative process of simulations were run to predict accurate bending parameters for the flexure bending mechanism.The FEM simulation demonstrated a result of an elliptically bent trapezoid mirror surface that fit with desired elliptical mirror profile within ±20 nanometers over 86% of the mirror’s measured length. The iteration process of model refinement, results of the finite element simulations, and preliminary test of the capacitive sensor array are discussed in this paper.